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\title{Northeastern University \\
  Department of Electrical and Computer Engineering \\
  - \\
  ECE4574 \\
  Final Report on the NorCal 40A} \\
\date{\today}
\author{
  Instructor: Professor David Brady \\
  - \\
  Authors: Paul Ozog, Brian Martins, Andrew Lai \\
}

\begin{document}

\begin{titlepage}
  \maketitle
  \thispagestyle{empty}
\end{titlepage}

\section{Introduction}
In this report, we will analyze the three amplifiers in the NorCal 40A transmit chain: the driver, buffer, and power amplifiers.  For each amplifier, we will analyze the type, class, power gain, and any information we feel is important in understanding the operation of the NorCal 40A.

\section{Gain Calculation}

The general expression for the power gain {\it G} (in dB) for each of the amplifiers in the transmit chain is given by:
\begin{equation}
  G = 10\;log \left( \frac{P_o}{P_i} \right)
  \label{eq:1}
\end{equation}
where 
\begin{math}
  P_o
\end{math}
and
\begin{math}
  P_i
\end{math}
are the power at the output and input of the amplifier, respectively [1].  

Note that the power figures in the following sections are taken from {\it The Electronics of Radio}, Figure 1.13 [2].  These values can be determined experimentally, however this requires desoldering certain components of the NorCal 40A, which we spent the last four months building.

\section{Buffer Amplifier}
The NorCal 40A buffer amplifier is a Class A source follower because the output is taken at the source of the JFET [2].  It's power gain (given by Equation \ref{eq:1}) is

\begin{equation}
  10\;log \left( \frac{300 \mu W}{10\mu W} \right) = 14.77\;dB
\end{equation}

\begin{figure}[h]
  \begin{center}
    \includegraphics[scale=0.660]{buffer.JPG}
    \caption{NorCal 40A Buffer Amplifier}
    \label{fig:buff}
  \end{center}
\end{figure}

This amplifier acts as a voltage buffer because the input impedance is infinite (so the amp draws little current) and the output impedance is low.  More accurately, the output impedance is the inverse of the JFET's transconductance, which is usually on the order of tens of millisiemens.  This gives the amplifier an output impedance of around 
\begin{math}
  50\Omega.
\end{math}

This combination of high input impedance and low output impedance makes the amplifier capable of providing the rest of the transmit chain the current it needs to operate.  This is important because the input to the buffer amp (the crystal oscillator) provides little current.

\section{Driver Amplifier}
The driver amplifier on the NorCal 40A transmit chain is a Class A common emitter amplifier with a transformer-coupled load [2]. This transformer is used to block DC voltages from being applied to the load, thereby increasing the amount of AC power delivered.  In theory, this technique results in an increase in the delivered power by a factor of two [3].  This is a common way of increasing the efficiency
\begin{math}
  \eta
\end{math}
of Class A amplifiers.

The driver amplifier's gain (using Equation \ref{eq:1}) is

\begin{equation}
  10\;\log \left( \frac{20 mW}{300\mu W} \right) = 18.24\;dB
\end{equation}

The input impedance of the driver is high so as to draw low current.  The output impedance will also be low, allowing the rest of the transmit chain to have a sufficient voltage.

The driver amp circuit is shown below:

\begin{figure}[h]
  \begin{center}
    \includegraphics[scale=0.83]{driver.JPG}
    \caption{NorCal 40A Driver Amplifier}
    \label{fig:driver}
  \end{center}
\end{figure}

\pagebreak

\section{Power Amplifier}
The power amplifier is the last in the transmit chain, and is a Class C common emitter [4].  Note that a harmonic filter is applied at the output to filter out the harmonics of the fundamental frequency.  Since the output of the amplifier is periodic, we may extract a sine wave of the pure fundamental frequency provided our filter has a sufficiently high Q-factor.

Because there is no DC biasing, the power amp has a relatively large efficiency, which is given by:

\begin{equation}
  \eta = \frac{V_{cc} - V_{on}}{V_{cc}}
\end{equation}

and clearly, 
\begin{math}
  V_{cc} 
\end{math}
is significantly larger than
\begin{math}
  V_{on}
\end{math}
so the efficiency is relatively high at 84\% (in theory).  However, according to Rutledge, the actual efficiency is more like 78\% [4].

The power gain of the NorCal 40A power amp is given by:

\begin{equation}
  10\;log \left( \frac{2.0\;W}{20 mW} \right) = 20.00\;dB
\end{equation}

\begin{figure}[h]
  \begin{center}
    \includegraphics{power.JPG}
    \caption{NorCal 40A Power Amplifier}
    \label{fig:power}
  \end{center}
\end{figure}

\pagebreak

\section{Conclusion}
By examining each of the three transmit amplifiers, we have shown that the overall gain (in linear scale) is on the order of 
\begin{math}
  10^6. 
\end{math}
This is to ensure that the oscillator's extremely low voltage gets amplified enough to drive a 2W antenna.  Though the buffer has a relatively low gain of 14.77 dB, it is crucial for providing current to the driver amplifier.  The driver amp, in turn, applies a significant 18.24 dB power boost.  The the power amp then provides 20.00 dB amplification, and finally the harmonic filter extracts the oscillator's fundamental sinusoid to drive the antenna. 


\section{Reference}
[1] D. Rutledge, ``Transistor Amplifiers'', {\it The Electronics of Radio}, Cambridge University Press, 1999, pp. 175-178.

[2] D. Rutledge, ``The NorCal 40A'', {\it The Electronics of Radio}, Cambridge University Press, 1999, pp. 18.

[3] D. Rutledge, ``Maximum Efficiency of Class-A Amplifiers'', {\it The Electronics of Radio}, Cambridge University Press, 1999, pp. 182-188.

[4] D. Rutledge, ``Power Amplifiers'', {\it The Electronics of Radio}, Cambridge University Press, 1999, pp. 182-188.


\end{document}
